The purpose of this paper is to investigate the four–parameter circular regression model of Taylor in which the angular error is distributed as a wrapped Cauchy distribution. The study is also extended to a polynomial circular model, including parameter estimation using a method of maximum likelihood. The estimations of regression parameters are examined through simulations. In addition, an application of the model considered here is illustrated using a real dataset of wind directions measured at a weather station in Texas and its fit is compared with some existing regression models